Accurate macromolecular structures using minimal measurements from X-ray free-electron lasers

Abstract

X-ray free-electron laser (XFEL) sources enable the use of crystallography to solve three-dimensional macromolecular structures under native conditions and without radiation damage. Results to date, however, have been limited by the challenge of deriving accurate Bragg intensities from a heterogeneous population of microcrystals, while at the same time modeling the X-ray spectrum and detector geometry. Here we present a computational approach designed to extract meaningful high-resolution signals from fewer diffraction measurements.

Figure 1. Thermolysin structure determination at 2.1 Å resolution

(a) 2mF_o−DF_c electron density contoured at 1 σ (gray mesh) with water molecules shown as red spheres. (b) mF_o−DF_c difference density map contoured at +3 σ (green mesh) and −3 σ (red mesh) showing binding sites for two of the four Ca ions and (c) the single Zn ion. (d) Detail of two crystal lattices found on the same diffraction image. Modeled spot positions assigned to the different lattices are shown in red and blue, respectively. The sample-detector distance of 135 mm corresponds to a resolution of 2.15 Å at the edges. (e) Detail from a different diffraction image. Increasing radial spot elongation is observed with distance from the beam center (blue cross).

Figure 2. Calibration and validation

(a) Aggregate relative positions (top) and rotations (bottom) of 32 pairs of application-specific integrated circuits (ASICs), each pair bump-bonded to a pixel array sensor of the CSPAD detector. The two ASICs on each sensor are manufactured to be aligned along the long axis, separated by a 3.0-pixel gap. These calibration results bear out this expectation within the tolerances shown. (b) Impact of positional accuracy on the indexing and integration success rate. Perturbing the ASICs away from their true positions reduces both the total number of indexed images (blue) and the number of images that contain successfully integrated reflections at high (1.8–2.2 Å) resolution (red). Error bars are the standard deviation from five different sets of perturbations drawn from a twodimensional normal distribution with a standard deviation σ_r. Separate perturbations were drawn for each ASIC. Squares: failure to apply final subpixel corrections from iterative least squares refinement. Circles: failure to apply nearest-whole pixel corrections. (c) Detail of four Bragg reflections on a thermolysin diffraction pattern, showing pronounced (seven pixel) radial elongation for the [27 –34 –7] reflection and lesser elongation for those nearby. Solution of Bragg’s law for each pixel (black arrows) identifies the spread of photon energies that contribute to each reflection. Red disks delineate integration masks from a three-parameter model with wavelength limits λ_high = 1.297 (9.556 keV) and λ_low = 1.313 (9.443 keV), and full-width mosaic spread δ = 0.174°. (d) Reciprocal space diagram indicating how different-shaped reflections arise. Reciprocal lattice points (arcs) all have a constant angular extent δ due to their mosaic spread. Points are in reflecting condition if they are within the zone between the high-energy (red) and low-energy (blue) Ewald spheres. Therefore, a greater fraction of the [27 –34 –7] mosaic distribution is within the reflecting condition, leading to a reflection that subtends a greater radial angle Δθ. (e) Paired refinements of the thermolysin structure. Red and green bars indicate the change in R_work and R_free, respectively, as higher-resolution data are added to the refinement. Dark and light blue bars show changes to the R-factors when the newly added high-resolution structure factors are randomly permuted. The data are interpreted as containing statistically significant signal for the resolution shells where ΔR_free is continuously negative, i.e. out to 2.1 Å.